Malament–Hogarth Machines and Tait’s Axiomatic Conception of Mathematics
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In this paper I will argue that Tait’s axiomatic conception of mathematics implies that it is in principle impossible to be justified in believing a mathematical statement without being justified in believing that statement to be provable. I will then show that there are possible courses of experience which would justify acceptance of a mathematical statement without justifying belief that this statement is provable.
- Alan B. Non-deductive methods in mathematics. In E. N. Zalta (Ed.) Stanford encyclopedia of philosophy (Fall 2013 Edn.). <http://plato.stanford.edu/archives/win2012/entries/davidson/>.
- Earman, J., & Norton, J. (1996). Infinite pains: The trouble with supertasks (Vol. 11, p. 271). Cambridge, Mass.: Blackwell Publishers.Google Scholar
- Earman, J., & Norton, J. D. (1993). Forever is a day: Supertasks in Pitowsky and Malament–Hogarth spacetimes. Philosophy of Science, 60(1), 22–42.Google Scholar
- Frege, G. (1980). The foundations of arithmetic: A logico-mathematical enquiry into the concept of number. Evanston, IL: Northwestern University Press.Google Scholar
- Kaye, R. (1991). Models of Peano arithmetic, volume 15 of Oxford logic guides. New York: Oxford University Press.Google Scholar